4088
Ind. Eng. Chem. Res. 2009, 48, 4088–4093
A Model To Predict the Concentration of Dispersed Solid Particles in an Aqueous Medium Confined inside Horizontal Cylindrical Channels Herbert Lorı´a* and Pedro Pereira-Almao Department of Chemical and Petroleum Engineering, Schulich School of Engineering, UniVersity of Calgary, Calgary, Alberta T2N 1N4, Canada
Carlos E. Scott Alberta Ingenuity Centre for In Situ Energy, UniVersity of Calgary, Calgary, Alberta T2N 1N4, Canada and Facultad de Ciencias, Escuela de Quı´mica, UniVersidad Central de Venezuela, Caracas 47102, Venezuela
The deposition of solid particles in cylindrical channels has received considerable attention, because of its direct application in industry. However, an adequate mathematical expression that studies the separation and suspension of dispersed particles present in horizontal cylindrical channels is still missing. In this paper, we developed and solved a time-dependent, two-dimensional convective-dispersive model that simulates the deposition and suspension of dispersed particles immersed in a fluid medium inside the cross section of a horizontal cylindrical channel in a stagnant situation. The results of the modeling are compared with a series of experiments that permit one to know the concentration of the particles in different points in the cross section of a horizontal cylinder. These experiments were performed using particles in the micrometer range dispersed in an aqueous medium. The conditions that permit to control the suspension and deposition of the particles inside a liquid medium with cylindrical geometry are unveiled by the presented model. 1. Introduction Mass transfer and deposition of fine particles in cylindrical channels is helpful in a wide variety of applications, such as aerosol classification and its deposition under electrical fields, in the formation of deposits in heat exchangers and pipelines, in hydrodynamic field chromatography, in the control of thrombus formation in organs, for ultradispersed catalysis, etc.1 A theoretical prediction of the particle deposition in such systems would be very useful for the design and optimization of these processes. The study of the particles behavior immersed in fluids began hundreds of years ago, when Archimedes introduced the concepts that made it possible to determine the forces acting on objects immersed in liquids.2 However, it was not until the last few decades when significant advancement was made in the understanding about particle sedimentation in vertical and horizontal channels. These advances began with the study of the motion and settling of a single rigid particle in various media and also under boundary layer effect.3 Forney and Spielman4 investigated the phenomenon of sedimentation of particles in vertical flow and gave expressions for the sedimentation velocity of particles for a wide range of particle diameters. Continuing with the works in vertical geometry, Shah et al.5 obtained measurements of concentration profiles and dispersion coefficients on gasliquid-solid column beds, later Kelkar and Shah6 expanded this work by collecting experimental dispersion coefficient data for continuous three-phase bubble columns. Sehmel7 and Yoshioka et al.8 reported their study on the settling of large particles (with diameters of >200 µm) in horizontal flow. Laurinat and Hanratty9 took into account the motion of the particles in different directions and proposed an empirical fit to a representative deposition flux profile as a function of the angle around * To whom correspondence should be addressed. Tel.: +1 403 210 95 90. Fax: +1 403 210 39 73. E-mail address:
[email protected].
the cylindrical channel cross section in horizontal flow. The determination of the driving forces present in the settling of particles immersed in fluids has been studied by Mols and Oliemans.10 They have modeled the dispersion and deposition as a combined process of diffusion and gravitational settling fluxes of particles in a one-dimensional problem between two horizontal plates. Based on these previous studies, it is important to emphasize that the sedimentation phenomenon in horizontal channels is more complex, in comparison to those in vertical channels, because of the effect of the gravitational force in the different orientation. Investigations have shown that, because of the gravitational pull, the sedimentation velocity of the particles in horizontal cylindrical channels is nonsymmetrical along the cross-section of the channels.11 It is generally believed that the sedimentation velocity in a horizontal cylindrical channel essentially depends on the fluid properties and the position of the particles around the channel cross section. Also, the effect of the gravitational force cannot be neglected. However, an adequate comprehensive physical model that evaluates the effect of the separation and suspension of the particles present in a horizontal cylindrical channel is still missing in the literature. The objective of this paper is to present a study on the mechanical separation and suspension of dispersed particles (particle diameters of 0.713, they were quantitatively diluted until the observed absorbance value was
